OFFSET
1,1
COMMENTS
For k > 2, the equation x^2 - k*y^4 = -1 has at most one positive integer solution. If this solution (x, y) exists, we have v = y^2, where v is the smallest integer satisfying the Pell equation u^2 - k*v^2 = -1 (A130227).
LINKS
Chen Jian Hua and Paul Voutier, Complete solution of the diophantine equation X^2 + 1 = dY^4 and a related family of quartic Thue equations, arXiv:1401.5450 [math.NT], 2014-2018.
EXAMPLE
The equation x^2 - 2*y^4 = -1 has only two positive solutions (1, 1) and (239, 13), so 2 is in the sequence.
CROSSREFS
KEYWORD
nonn
AUTHOR
Jinyuan Wang, Aug 09 2022
STATUS
approved